The student pilot stated that in preparation for his solo cross-country flight, he reviewed his flight planning with his flight instructor. He said he flew to the destination airport, where he performed one approach and landing, followed by flight maneuvers north of the airport, and then landed. The pilot shut the airplane down to use the restroom. Prior to departure from the destination airport, he did not visually check the airplane fuel level through the fuel filler ports. During the return flight, he visually observed the fuel quantity and was decreasing rapidly, and he decided to land at an alternate airport. During the approach to the alternate airport, the engine sputtered and lost power. He landed the airplane with a tailwind and strongly applied the brakes to try to slow the airplane down as soon as possible. The airplane overran the runway and impacted a fence and construction equipment that resulted in substantial damage to both wings. Postaccident examination of the airplane revealed no useable fuel in the airplane fuel tanks.